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1699is an odd number,as it is not divisible by 2
The factors for 1699 are all the numbers between -1699 and 1699 , which divide 1699 without leaving any remainder. Since 1699 divided by -1699 is an integer, -1699 is a factor of 1699 .
Since 1699 divided by -1699 is a whole number, -1699 is a factor of 1699
Since 1699 divided by -1 is a whole number, -1 is a factor of 1699
Since 1699 divided by 1 is a whole number, 1 is a factor of 1699
Multiples of 1699 are all integers divisible by 1699 , i.e. the remainder of the full division by 1699 is zero. There are infinite multiples of 1699. The smallest multiples of 1699 are:
0 : in fact, 0 is divisible by any integer, so it is also a multiple of 1699 since 0 × 1699 = 0
1699 : in fact, 1699 is a multiple of itself, since 1699 is divisible by 1699 (it was 1699 / 1699 = 1, so the rest of this division is zero)
3398: in fact, 3398 = 1699 × 2
5097: in fact, 5097 = 1699 × 3
6796: in fact, 6796 = 1699 × 4
8495: in fact, 8495 = 1699 × 5
etc.
It is possible to determine using mathematical techniques whether an integer is prime or not.
for 1699, the answer is: yes, 1699 is a prime number because it only has two different divisors: 1 and itself (1699).
To know the primality of an integer, we can use several algorithms. The most naive is to try all divisors below the number you want to know if it is prime (in our case 1699). We can already eliminate even numbers bigger than 2 (then 4 , 6 , 8 ...). Besides, we can stop at the square root of the number in question (here 41.219 ). Historically, the Eratosthenes screen (which dates back to Antiquity) uses this technique relatively effectively.
More modern techniques include the Atkin screen, probabilistic tests, or the cyclotomic test.
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